[EM] Salva presents an example

[Donald E Davison]

  ----------- Forwarded Letter -----------
From: Salva
To: "Donald E Davison" <donald at mich.com>
Subject: Re: Salva Voting - multi-seat example
Date: Sat, 17 Apr 1999 02:19:35 +0200

>I suggest that you ask Mr. Salva to give you a complete example of his
>proposed method with at least 3 seats.

OK, here we go:
there is a district with 10 seats. 6 parties are running for them. After
counting the first choice of all the cast ballots the results are
A 39%
B 28%
C 16%
D 10%
E    4%
F   3%

party A gets 4 seats, party B gets 3 seats, C gets 2, D gets 1 and E and F
none. This is a provisional result. Now we take all the ballots that had E
and F as a first choice (7%) and look at their second choice. Second choice
of those ballots is as follows:
A 0%
B 50%
C 0%
D 0%
E 25%
F 25%

so a 50% of a 7% of votes are transferred to party B, thus party B has now
31.5%
instead of 28%. The new provisional result may still be A4, B3, C2, D1 and E
and F none. Now we take all the ballots that in their second choice voted
for E and F (50% of the remaining after the first count, 3.5% of the total
number of ballots) and look what's their third choice.
the result is
A 0%
B100%
C 0%
D 0%
E 0%
F 0%

now the situation is
A 39%
B  35%
C 16%
D 10%
E    0%
F   0%

and the allocation of seats is A4, B4, C1, D1, E0 and F0. Now the result is
the definitive one, as all ballots are allocated to a party with
representation.
It might have happened that party D didn't obtain any seat after the third
count. Then we take those 10% of ballots and relocate them by their second
choice, and E and F would still have a chance to have representation (maybe
not in this example, but the point is that no candidate is definetively left
out untill the very end).
It is necessary for multy-seat districts to allocate seats after each count,
to determine which parties obtain representation and which ones don't. What
I mean is that a party with 9% of votes could obtain representation
depending on the distribution of the rest of votes or a party with 11% could
not, so you cannot work only with percentages or votes during the process.
Is everything clear now? If you have any doubt just ask.

>but I do not understand how it is like STV.

ok, I was wrong I supose. I saw the similarity in that you rank candidates
and in that all ballots end up in a seat. I supose you are right in that the
diferences are more than similarities...

>    This example will have eleven candidates running in a four member
district.
>    The first count of the ballots is as follows(xx means lower choices):
>
> Axx   Bxx   Cxx   Dxx   Exx   Fxx   Gxx   Hxx   Ixx   Jxx   Kxx
> 80    78    76    74    72    70    68    66    64    62    60 = 770
>
>     As of now, candidates A-B-C-D are the lead candidates. The second
>choices of candidates E to K would receive a vote each and then be
>transferred(added) to the count of the first choices. Suppose the following
>second choice votes:
>
> 50    48    45    43    50    41    41    39    37    35    33 = 462
>---   ---   ---   ---   ---   ---   ---   ---   ---   ---   ---
>130   126   121   117   122   111   109   105   101    97    93
>
>    Now the leading four candidates are A-B-E-C
>    The next step is to repeat the routine by giving a vote to the next
>available choice of each ballot of candidates D,F,G,H,I,J,K
>    The next available choice of the ballots of candidate D is the second
>choice.
>    The next available choice of the ballots of candidates F,G,H,I,J,K are
>the third choices.
>
>    This routine keeps repeating until there are no more available choices
>remaining.


YES you have perfectely understood the method, I'm very glad you did because
my English is poor and sometimes I'm not sure if I make myself understood

>    Whichever four candidates are now in the lead, those four are the
>elected members from this district.

this is not necessarily so. It is true when the candidates are individuals,
but if they are parties then all seats can end up in a single candidate or
2-1-1 or 2-2 or 3-1

I would like to note that in a single-winner election the process could be
very long because the candidate receiving the highest number of votes could
be changing in many counts in a row untill it is reached an stabilization of
a
candidate receiving many votes. On the other hand the process can
be shortened because once a candidate has more than 50% it can not be
defeated. It is also important to note that in a single-winner election many
ballots, obviously, don't end up with representation, which was my original
porpose. Well, indeed, in multy-seat elections it could happen some ballots
ending up without representation if they don't have the whole ranking filled
up, but that's the voter fault, not the method.

Salva